(x – 2)2 + y² = c² %3D

Q: (c) Sketch some typical members of the family of curves y = ax? + b.

A: Given the curves y=ax2+b is parabola  For a=1, b=0 y=x2

Q: 2. 3x + 4y +c = 0

A:

Q: 1 find the length of the curve x = 7y* + y2, from y = 1 to 24 y = 2.

A:

Q: Find the length of the curve y = xVa 0 <x < 1.

A:

Q: I Find the acute angle between the two curves xy = 3 and x2 = 9y

A: Given data: First curve xy=3. Second curve x2=9y.

Q: Sketch the ff curves: a) Y = x² e* b) Y = 1+lnx c) Y = ²-4)² x-4

A: To draw the graph of asked curves you can simply make a table and find some points through the curve…

Q: Find the exact length of the curve. y4 1 X = 8 1sy< 3 4y2"

A: Here the formula of length of the curve is:

Q: Sketch the following family of curves. 1. 3x + cy – 12 = 0 %3D

A:

Q: Find the equation of y, glven the derlvative and the Indicated polnt on the curve. dy = 2x- 1 xp

A:

Q: The parabola y = x2 + C is to be tangent to the line y = x. Find C.

A: To find the value of C.

Q: Find the point in the first quadrant on the curve y = x + x - l closest to the origin.

A:

Q: Consider the curve given by the equation 0 = y3 +xy +2ax + 1+x4  y'(0) = ?

A: Answer and explanation is given below

Q: Find the coordinate of the extrema of the curve y = x² – 4x + 1.

A:

Q: Sketch the following curve y f(x, y) = x² + 1

A: Given function, fx,y=yx2+1 To sketch the curve of the function.

Q: b) Find the point on the curve y Vr that is closest to the point (7,0).

A: Find the point to the curve y=(x)^(1/2) that is closest to the point (7,0)

Q: I Discuss the properties of the curve and sketch fully: a) y = x² e-x 1+lnx b) y = -

A:

Q: Find the exact length of the curve. Vy (y - 3), 16 < y < 25 X =

A:

Q: Find the exact length of the curve y=1+6x% for 0<xsl

A: We have to find the exact length of the curve y=1+6x32 for 0≤x≤1.

Q: Find the point on the curve y2 =;(x + 1) which is nearest the origin.

A: If (x, y) is any point on the curve nearest the origin then the square of its distance from the…

Q: Sketch the two curves 7(t) = tî + t²j; t e [1, 5] and B(T) = e"î + e²r3; T E [0, In 5]. How are they…

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Q: Find the point on the curve y2 =(x+1) which is nearest the origin.

A:

Q: For the curve y=ax^3+bx^2+12x-7, what values of a and b will make the tangent to the curve at x=2…

A:

Q: Find the length of the curve given by x(t) = 1 + 3t² ,y(t) = 4 + 2t³, 0 <t < 1.

A: xt=1+3t2yt=4+2t3 Differentiate the above equation w.r.t."t"…

Q: Find the exact length of the curve. y = (1 + x2)3/2, 0 < x < 2

A:

Q: Find the exact length of the curve.   y = 1+ 6x3/2 , 0 ≤ x ≤ 1

A: Find the exact length of the curve.

Q: The family of curves orthogonal to x2 + 4y2 = c2 has the general equation 04. %3D

A:

Q: Find the exact length of the curve. X = 8. 1sys 2 4y2'

A:

Q: Find the exact length of the curve. y2 = 16(x + 3)3,   0 ≤ x ≤ 3,  y &gt; 0

A: Given: Find the exact length of the curve.

Q: Find the exact length of the curve. 1 + 1sys 2 8 4y2

A:

Q: Sketch the following curves. 33. y = 2x + 3x2 + 1 %3D

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Q: Find the length of the curve defined by from = 9 to z = 10. 2 y-4lm (()²-1) =

A: find derivative

Q: Find the exact length of the curve. y2 = 16(x + 4)3, osxs 2, y > 0

A: Given data:   The given expression is y2=16(x+4)3. The given limits of x is [a,b]=[0,2].   The given…

Q: Evaluate (2 - xy) ds where C is the curve given below. -2 -1 -2

A: Given   ∫C2-xyds Curve C

Q: 6x 4. У3 y = х+3

A:

Q: Find the exact length of the curve. x3 y = 1 < x < 2 %3D 4x

A: y=x33+14x  ,  1≤x≤2.

Q: Sketch the curves below by eliminating the parameter t. x = V3t + 4, y = 3t + 2

A: Given query is to sketch the curve by removing t.

Q: 3x + xy? 2y + x?y dy dx

A:

Q: I Discuss the properties of the curve and sketch fully: a) y = x² e-x

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Q: Find the exact length of the curve. x = (2y + 1)3/2, 0<y<3

A: Differentiating with respect to y, we get

Q: For the curve y = ax3 + bx2 + 12x - 7, what values of a and b will make the tangents to the curve at…

A: We have to find the value of a and b according to the given information

Q: Find the exact length of the curve. y = = 0 < x < 6

A:

Q: Find the exact length of the curve. x = 8 4y2' 1sys 2

A: Given, x=y48+14y2,1≤y≤2

Q: Find the coordinates of the point in the curve y = 12x – 2y + 23 that is nearest to the point P(10,…

A: Given curve: y2=12x-2y+23 The point is  P10,4 To find: The coordinates of the point on the curve…

Q: Find the exact length of the curve. y = x2 - In(x), 1 < x < 4

A:

Q: s to the curve y = x* at the %3D

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Q: Consider the two graphs y= 2x and x2 - xy + 2y = 28. The absolute value of the tangent of the angle…

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Q: How far from the x-axis is the center of the curve 2x2 – 2y2 + 10x – 6y – 55 = 0?

A: The given equation of the curve is: 2x2 – 2y2 + 10x – 6y – 55 = 0 This can be written as:

Q: 4. (x – h)? + y² = c²

A: The solution are next step

Q: Find the exact length of the curve. Y=y4/8 + 1/4y2, 1 less than or equal to Y less than or equal 2.

A: Given: Y=y48+14y2 , 1≤y≤2 As, the length of the curve, L is given by: L=∫ab1+dydx2dx According to…

Q: Consider y = x2+3 /3e4x^2. Find the value of x at which this curve has a stationary point

A: Consider the given function.